GROWTH AND MATURITY OF SALMON IN THE OCEAN 27 
CORRELATION BETWEEN SIZE OF EGGS AND SIZE OF FISH 
A careful examination of the data has been niade in order to determiae to what 
extent the size of the eggs is correlated with the size of the fish, and, further, the 
extent to which this factor may tend to produce the observed differences in egg 
sizes. 
A very definite positive correlation is found to exist between the size of the eggs 
and the size of the fish when fish of the same age group and the same degree of 
maturity are considered. The coefficient of correlation (r) has been computed for 
two typical distributions — one of mature and the other of immature fish. Table 2 
shows the correlation between the size of fish and the size of eggs in 66 females in 
their fourth year, ocean nuclei, which were taken by troll off the mouth of the Colum- 
bia River, August 13, 1919. There are obviously two distinct groups represented 
in this tabulation, which are readily distinguishable on the basis of egg size. One 
group of 63 individuals, in which the logarithm of the diameter of the eggs is greater 
than 0.55, and another containing only three individuals, in which the logarithm 
is less then 0.35. The group with the larger eggs is mature and the coefficient of 
correlation between size of eggs and length of fish was found to be 0.6210 ±0.0531, 
a high positive correlation. 
Table 2. — Chinook salmon taken by troll off the mouth of the Columbia River, August IS, 1919 
Females in their fourtb year and which migrated as fry (scales with ocean nuclei) tabulated to show correlation between length 
and size of eggs 
Logarithms of diameter of eggs 
(mid-value of class) 
Centimeter length (mid-value of class) 
Total 
77 
79 
81 
83 
85 
87 
89 
91 
93 
95 
97 
99 
101 
103 
105 
107 
0.29 
1 
1 
2 
1 
2 
2 
1 
3 
7 
6 
2 
2 
8 
4 
7 
11 
6 
2 
.33* _ 
1 
.57".._ 
1 
1 
.59 
1 
1 
1 
.61 - 
.63 
1 
1 
2 
1 
2 
.65 -.- 
1 
1 
.67 _ 
1 
1 
1 
1 
.69 _ 
1 
1 
.71 
1 
.73 _ 
1 
4 
1 
1 
.75 
1 
1 
1 
2 
1 
.77..,. 
1 
2 
1 
1 
.79 _ 
2 
2 
2 
1 
1 
1 
1 
1 
1 
.81 
.83 
Total 
3 
3 
2 
I 
2 
3 
9 
8 
5 
12 
5 
4 
2 
2 
2 
66 
1 
Note. — In this and all other tables of this report an asterisk (*) has been used to mark a break in the continuity of the 
table. It indicates that one or more classes have been omitted from the natural sequence just preceding the class marked. 
A double asterisk (*') is used to mark such breaks as are of particular signifioance. 
The coefficient of correlation between size of eggs and size of fish has likewise 
been determined for a group of 36 immature females in their third year, ocean 
nuclei, taken in Monterey Bay, June 19 to 21, 1918. The data showing the dis- 
tribution according to size of eggs and length of fish of aU the females of this age group 
contained in the collections are given in Table 3. Two distinct groups, which are 
well separated on the basis of egg size but overlap almost completely in length, 
are also shown in this tabulation. The coefficient of correlation for the immature 
group is 0.7680 ±0.0461. 
